1. Field of the Invention
The invention relates to an optical waveguide, more particularly, to an optical waveguide made from a ferroelectric material and having a chirp grating capable of providing high wavelength conversion efficiency.
2. Description of the Related Art
Referring to FIG. 1, a typical quasi-phase matched optical waveguide 1 includes a substrate 11 made from a ferroelectric material, such as LiNbO3.
To fabricate the waveguide 1, an aluminum grating pattern 12 is deposited on a first surface 111 of the substrate 11 through a suitable technique such as vacuum vapor deposition. The aluminum grating pattern 12 includes a plurality of parallel aluminum strips having the same width. A photoresist 13 is present in the gaps between the aluminum strips. The first surface 111 and the aluminum grating pattern 12 are covered by a conductive liquid layer 14, such as a LiCl liquid layer. The second surface 112 of the substrate 11 is covered by another conductive liquid layer 14′.
When an electric field is applied to the conductive liquid layers 14, 14′, regions of the substrate 11 beneath the contact surface areas of the first surface 111 and the aluminum grating pattern 12 are affected by the electric field and become domain-inverted regions which are referred to as first polarization parts 113. Regions of the substrate 11 beneath the contact surface areas of the first surface 111 and the photoresist 13 are not affected by the electric field. These regions are referred to as second polarization parts 114 hereinafter. A quasi-phase-matched periodic grating 116 (FIG. 2) composed of the first and second polarization parts 113, 114 is thus formed. When the electric field intensity is decreased slowly, the polarity of the first polarization parts 113 does not change any more.
Referring to FIG. 2, when the polarization of the substrate 11 becomes stable, the electric field, the aluminum grating pattern 12, the photoresist 13 and the conductive liquid layers 14, 14′ are removed, and the first surface 111 is covered with a mask 9 containing chromium. A middle part of the mask 9 has a first shield portion 91 with a width (W), and the remaining parts are second shield portions 92. Only the second shield portions 92 are plated with chromium. When the substrate 11 together with the mask 9 is dipped into a benzoic acid solution at a temperature of 200° C. for one hour, parts of the substrate 11 covered by the second shield portions 92 do not react with the benzoic acid solution. However, the part of the substrate 11 covered by the first shield portion 91 undergoes a proton-exchange reaction with the benzoic acid solution as follows:LiNbO3+C6H5COOH→Li1-xHxNbO3+(C6H5COOLi)x 
After reaction, the part of the substrate 11 covered by the first shield portion 91 of the mask 9 is formed into a waveguide part 18 which is parallel to the periodic grating 116 formed on the substrate 11. The mask 9 is then removed, and the substrate 11 is annealed slowly at 450° C. for about one hour. The resulting waveguide part 18 has an inner surface with a refractive index up to 0.1-0.15 which is higher than that of the remaining parts of the substrate 11.
As the aluminum strips of the aluminum grating pattern 12 are equal in width, the first polarization parts 113 have the same width. Further, since the aluminum strips are equally spaced apart from each other, the second polarization parts 114 also have the same width. Therefore, the waveguide 1 has a uniform grating period Λ0 which is the sum of the width of one first polarization part 113 and the width of one second polarization 114.
When a light signal is launched into the quasi-phase matched period grating 116 of the waveguide 1, by properly adjusting the incident angle of the light signal, the light signal can be transmitted by reflection through the waveguide part 18. As the light signal passes through the waveguide part 18, it produces a second harmonic wave which interacts with a new signal wave (a coupling component) to generate a conversion wave.
FIG. 3A shows plots (A) and (B) which were obtained by launching a signal wave with a pulse width of 6 picoseconds into the waveguide 1 having a uniform grating period (Λ0=14.754 μm). Chromatic dispersion of lithium niobate is not taken into consideration in plot (A) (i.e., refractive index is 1). Plot (B) takes into consideration the chromatic dispersion. Plot (B) which is close to plot (A) demonstrates that the wavelength conversion energy of plot (B) does not reduce much compared to that of plot (A) for the pulse width of 6 picoseconds.
However, referring to FIG. 3B, when the pulse width is reduced to 0.6 picosecond, plot (B) which takes into consideration chromatic dispersion shows that the wavelength conversion energy is reduced to nearly zero. The reduction of the wavelength conversion efficiency is due to a phenomenon of back conversion resulting from the chromatic dispersion of the substrate 11. The conversion efficiency reduction becomes serious when the pulse width of a launched signal wave is decreased in order to increase the speed of an optical system.
The phenomenon of back conversion is affirmed by the inventor of this application in Shih-Chiang Lin, “Enhanced Cascade X(2) SHG+DFG Interactions Based on Chirp Period Quasi-Phase-Matched Waveguide,” Conference on Lasers and Electro-Optics (CLEO), 2007. In order to increase the wavelength conversion energy, a chirp waveguide to retard and alter the relative phase accumulation is proposed in this reference. The chirp waveguide enhances the conversion efficiency up to 170%, and has a normalized grating period which increases exponentially and decreases stepwise in an alternating fashion. However, as the propagation distance increases, the normalized grating period varies non-exponentially as shown in FIG. 4.
Ole Bang, Carl Balslev Clausen, Peter L. Christiansen and L. Torner, “Engineering Competing Nonlinearities,” Opt. Lett., Vol 24, pp. 1413-1415, 1999, discloses a chirped quasi-phase matched waveguide having a chirped grating which satisfies the following equation:Λ(x)/Λ0=1.0026−0.0026·sin(K2·x)  (1)where Λ(x)/Λ0 denotes a normalized grating period, Λ0 is a grating period at a propagation distance of zero, Λ(x) is a grating period at a propagation distance of (x), and K2 is 1.1×103 (l/m). The normalized grating period designed by Ole Bang et al varies sinusoidally.